# Problem of Harmonics

1. Apr 15, 2010

### jackleyt

1. The problem statement, all variables and given/known data

One end of a horizontal string is tied to a wall, and the other end is tied to an object with weight W that hangs over a pulley to hold the string taut. The object is large enough that the string never moves at the pulley. Under these conditions, the string vibrates with wavelength lambda and frequency f in its first harmonic.

If we add enough weight to double W without appreciably stretching the string, what will be the wavelength (in terms of lambda and f) of the string's first harmonic vibration?

If we add enough weight to double W without appreciably stretching the string, what will be the frequency (in terms of lambda and f) of the string's first harmonic vibration?

If we do not change W, but move the pulley so that the vibrating part of the string is half as long, what will be the wavelength (in terms of\lambda and f) of the string in its first harmonic?

2. Relevant equations
v=lambdaf v=sqrt(F/(m/L)) lambda=(2L)/n

3. The attempt at a solution

Having a hard time deciphering what the question is asking, or how to get there.

2. Apr 15, 2010

### AtticusFinch

Re: Harmonics

The question is asking you to find new values in terms of the old wavelength and frequency.

For the first and second part, what would adding weight increase?

For the third part, what does first harmonic mean in terms of wavelength?